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# At a certain department store present-wrapping counter, each

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Senior Manager
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At a certain department store present-wrapping counter, each  [#permalink]

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Updated on: 20 Oct 2013, 09:56
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95% (hard)

Question Stats:

45% (02:37) correct 55% (02:40) wrong based on 392 sessions

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At a certain department store present-wrapping counter, each clerk will wrap no fewer than twenty and no more than thirty presents per hour. If seventy people are standing in line, will all of their presents be wrapped after one hour?

(1) Each person in line has at least one present to be wrapped by one of the six clerks at the counter.
(2) If each person in line had one more present to be wrapped, nine clerks would be required to guarantee that every present would be wrapped in one hour.

Originally posted by chiragr on 08 Feb 2006, 01:16.
Last edited by Bunuel on 20 Oct 2013, 09:56, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: At a certain department store present-wrapping counter, each  [#permalink]

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20 Oct 2013, 10:21
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At a certain department store present-wrapping counter, each clerk will wrap no fewer than twenty and no more than thirty presents per hour. If seventy people are standing in line, will all of their presents be wrapped after one hour?

Say each clerk can wrap x presents per hour. We are given that $$20\leq{x}\leq{30}$$.

(1) Each person in line has at least one present to be wrapped by one of the six clerks at the counter. From that we can get that the number of presents to be wrapped is at least 70 and that there are 6 clerks at the counter. Now, the number of presents 6 clerks can wrap in an hour is $$120\leq{x}\leq{180}$$. Still not sufficient to answer the question: if the # of presents is 70, then the answer would be YES but if the # of presents is greater than 180, then the answer would be NO. Not sufficient.

(2) If each person in line had one more present to be wrapped, nine clerks would be required to guarantee that every present would be wrapped in one hour.

Say 70 people in line have total of n presents. We are told that n+70 presents can be wrapped by 9 clerks. 9 clerks can for sure wrap 9*20=180 presents. Thus we are given that $$n+70\leq{180}$$ --> $$n\leq{110}$$. So, there are at most 110 presents to be wrapped.

To guarantee wrapping 110 presents minimum 6 clerks are needed (6 slowest clerks can wrap 120 presents). We don't know how many clerks are there at the counter. Not sufficient.

(1)+(2) From (1) we know that there are 6 clerks, thus they can for sure wrap minimum 120 presents, since the # of presents is less than or equal 110, then these 6 can wrap all the presents. Sufficient.

Hope it's clear.
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08 Feb 2006, 19:16
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Hi,
=======================================
At a certain department store present-wrapping counter, each clerk will wrap no fewer than 20 and no more than 30 presents per hour. If seventy people are standing in line, will all of their presents be wrapped after one hour?
=======================================
So the slowest clerk can wrap 20 gifts
As a worst case the number of gifts wrapped in an hour is
20 * number of clerks.

=======================================
(1) Each person in line has at least one present to be wrapped by one of the six clerks at the counter.
=======================================
This does not give the number of gifts, hence is insufficient.

=======================================
(2)If each person in line had one more present to be wrapped, nine clerks would be required to guarantee that every present would be wrapped in one hour.
=======================================
This means that if there are 70 more gifts, nine clerks are needed.
If you can guarantee that 9 slow clerks can wrap all gifts in an hour, you can pretty much say any combination of clerks, slow or fast can do it within an hour.

Total number of gifts + 70 <= 9clerks * 20 Gifts wrapped by each
Total number of gifts <= 180 - 70
<= 110

However (2) does not give the number of clerks at the counter, hence is insufficient.

Using (1) and (2) together -
Number of clerks = 6

Assume all 6 clerks are slow; They can wrap 120 gifts in an hour.
Since we have 110 or less, this can be done.

##### General Discussion
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08 Feb 2006, 01:31
70 People
M clerk
N Present

1) Six Clerks No info about Presents ---Insufficient
2) Nine Clerks will guarantee N+70 presents
a. No Info about N so Insufficient

1+2 :
Analyze second in detailsâ€¦
9 Clerks =>

Min Number of packets (9*20 =180)
Max No of packets (9*30 =270)

So N can range from (180-70, 270-70) = (110, 200)

6 clerks Min wrap packets (6*20 = 120)
6 clerks Max wrap packets (6*30 = 180)

Hence if there are more than 180 packets this condition is not satisfied

Off course this is wrong otherwise I wouldnâ€™t be posting this question

----------------------------------------
OA is C:

9 people can wrap at least 9*20 = 180 presents
One more present per person so 180-70 = 110 Present

1 Says we have 6 clerks 1+2 can answer question!

Any one agrees or this is Kaplanâ€™s Mistake!
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08 Feb 2006, 02:37
1
agree with C)
from stem we know that one clerk can wrap 30 gifts at most per hour. Seventy people on the line,
From A we know that there are six clerks and minimum 70 presents which is insufficient
From B) we can calculate the number of gifts in the people on the line 9x30=270-70=200 approx. but we do not know how many clerks are currently working
combining both it is clear that 270-70=200 presents hold the people in the line, currently there are 6 clerks working who can pack 30 gifts at most, so the clerks will not be able to complete the job in one hour
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08 Feb 2006, 03:21
I actually find this question confusing. Please correct me if I'm wrong.

Combining (1) and (2) we know that:
if (2) assumes that a clerk can wrap 20 gifts per hour, then we have 9*20=180, but since the customers have 1 more, subtract 70 ->110
if (2) assumes that a clerk can wrap 30 gifts per hour, than we have 9*30=270, ->200

If there are six clerks and they work at 20 g/h, in the case of 110 they would be able to wrap all the gifts, otherwise they wouldn't.
Attachments

gifts.JPG [ 13.06 KiB | Viewed 6431 times ]

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08 Feb 2006, 09:31
thearch wrote:
I actually find this question confusing. Please correct me if I'm wrong.

I also found this confusing... and my analysis was same as yours!

BG if you see my explaination of OA says C for different reason than your analysis!
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08 Feb 2006, 22:08
Yeah I think cool frequency has given an good explanation... it is C
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20 Oct 2013, 09:47
coolfrequency wrote:
This means that if there are 70 more gifts, nine clerks are needed.
If you can guarantee that 9 slow clerks can wrap all gifts in an hour, you can pretty much say any combination of clerks, slow or fast can do it within an hour.

Total number of gifts + 70 <= 9clerks * 20 Gifts wrapped by each
Total number of gifts <= 180 - 70
<= 110

However (2) does not give the number of clerks at the counter, hence is insufficient.

Using (1) and (2) together -
Number of clerks = 6

Assume all 6 clerks are slow; They can wrap 120 gifts in an hour.
Since we have 110 or less, this can be done.

I am lost on this one. Kaplan has a very similar solution noted too.
However, instead of slowest case scenario, if I take the highest numbers:
Total number of gifts + 70 <= 9clerks * 30 Gifts wrapped by each
Total number of gifts <= 270 - 70
<= 200

Using (1) and (2) together -
Number of clerks = 6
Maximum gifts that can be wrapped 6 clerks: 6*30 = 180.

Which contradicts the slow case and so the answer to the main question will be E.

What am I missing?
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Re: At a certain department store present-wrapping counter, each  [#permalink]

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20 Oct 2013, 11:27
2
Thanks Bunuel
What I don't understand is, why did you choose the minimum speed as opposed to maximum in your calculation for n
You used: n+70 <= 180
Why not: n+ 70 <=270

The statement says 9 clerks can wrap n+70 presents at a speed of between 20...30 presents per hour. Why choose 20 and not 30?
Is it because of the use of the word "guarantee" in statement 2?
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Re: At a certain department store present-wrapping counter, each  [#permalink]

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20 Oct 2013, 11:31
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portland wrote:
Thanks Bunuel
What I don't understand is, why did you choose the minimum speed as opposed to maximum in your calculation for n
You used: n+70 <= 180
Why not: n+ 70 <=270

The statement says 9 clerks can wrap n+70 presents at a speed of between 20...30 presents per hour. Why choose 20 and not 30?
Is it because of the use of the word "guarantee" in statement 2?

Absolutely. We need to guarantee that every gift will be wrapped, thus we must consider that the clerks work at the slowest possible rate.
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Re: At a certain department store present-wrapping counter, each  [#permalink]

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20 Oct 2013, 11:54
Ah! Damn important words hidden in plain sight.

Thanks Bunuel
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Re: At a certain department store present-wrapping counter, each  [#permalink]

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23 Dec 2018, 08:32
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chiragr wrote:
At a certain department store present-wrapping counter, each clerk will wrap no fewer than twenty and no more than thirty presents per hour. If seventy people are standing in line, will all of their presents be wrapped after one hour?

(1) Each person in line has at least one present to be wrapped by one of the six clerks at the counter.
(2) If each person in line had one more present to be wrapped, nine clerks would be required to guarantee that every present would be wrapped in one hour.

Given: At a certain department store present-wrapping counter, each clerk will wrap no fewer than twenty and no more than thirty presents per hour.

Target question: If seventy people are standing in line, will all of their presents be wrapped after one hour?

Statement 1: Each person in line has at least one present to be wrapped by one of the six clerks at the counter.
Since we aren't told the MAXIMUM number of presents each person has, there's no way to answer the target question.
To see what I mean, consider these two conflicting scenarios:
Case a: Each person in line has 1 present. So, there are 70 presents to be wrapped by 6 clerks. Since each clerk can wrap AT LEAST 20 presents (for a total of 120 presents), the answer to the target question is YES, all of the presents will be wrapped after 1 hour
Case b: Each person in line has 1 trillion presents. Here, the answer to the target question is NO, all of the presents will NOT be wrapped after 1 hour
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: If each person in line had one more present to be wrapped, nine clerks would be required to guarantee that every present would be wrapped in one hour.
Here, we aren't given any information about the actual number of clerks.
Consider these two conflicting scenarios:
Case a: There are 9 clerks available. If 9 clerks can wrap all of the presents in the hypothetical situation in which everyone has 1 EXTRA present, then 9 clerks will definitely be enough to wrap the presents. In other words, the answer to the target question is YES, all of the presents will be wrapped after 1 hour
Case b: There is are ZERO clerks available (all on lunch break). Here, the answer to the target question is NO, all of the presents will NOT be wrapped after 1 hour
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Let T = the TOTAL number of presents to be wrapped
IF each of the 70 people in line had one more present, then there WOULD be T + 70 presents to be wrapped
Since each of the 9 clerks can wrap AT LEAST 20 presents per hour, they can wrap AT LEAST 180 presents.
So, we can write: T + 70 < 180
Subtract 70 from both sides to get: T < 110
So, statement 2 is telling us (indirectly) that there are fewer than 110 presents to be wrapped

Statement 1 tells there are 6 clerks.
Since each clerk can wrap AT LEAST 20 presents in one hour, they can can wrap AT LEAST 120 presents in total.
Since statement 2 tells us that there are FEWER THAN 110 presents, the answer to the target question is YES, all of the presents will be wrapped after 1 hour
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
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Re: At a certain department store present-wrapping counter, each   [#permalink] 23 Dec 2018, 08:32
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